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I am trying to understand how the length and diameter of a compartment are specified. For example, in the Hodgkin–Huxley model, we only have conductances specified in $\rm mS/cm^2$. How do you specify that a compartment is say $100 \mu\rm m$ long?

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I'm pretty sure basic Hodgkin-Huxley doesn't take into account distances or volumes, rather the spatial quantities in the units are derived from electrical properties. There is a related idea called Cable Theory that I believe does incorporate distance factors. –  Tim Jul 31 at 17:37

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